In order to properly evaluate the effective diagrams, we have to convert them in a QFT amplitudes language.
In general, within the EFT approach, since the sources (black lines) are static and do not propagate, any gravity amplitude of order \(G_N^l\)  can be mapped into a \((l-1)\) -loop 2-point function (as first noticed in [1]}) with massless internal lines and external momentum \(p\) , where \(p^2=s\ne 0\) :
\(\begin{tikzpicture}[baseline=(current bounding box.center)]\begin{feynman}(a);[right=0.5cm of a] (a2);[right=0.5cm of a2] (a3);[right=0.25cm of a3] (b1);[right=0.5cm of a3] (a4);[right=0.5cm of a4] (a5);[right=0.5cm of a5] (a6);[below=1.2cm of a] (e);[right=0.5cm of e] (e2);[right=0.5cm of e2] (e3);[right=0.5cm of e3] (e4);[right=0.25cm of e3] (b2);[right=0.5cm of e4] (e5);[right=0.5cm of e5] (e6);* {(a) -- [thick] (a6),(e)-- [thick] (e6),};\end{feynman}[gray] (a2) rectangle (e5);\end{tikzpicture} \qquad \Leftrightarrow \qquad \begin{tikzpicture}[baseline=(current bounding box.center)]\begin{feynman}(a);[below=0.4cm of a] (a2);[below=0.5cm of a2] (c);[below=1cm of a2] (a3);[below=0.4cm of a3](a4);* {(a) -- [thick] (a2),(a3)-- [thick] (a4),};\end{feynman}[gray,fill=gray] (c) circle (.6cm);\end{tikzpicture}\) 
